Suppose u=(1,−2,6)  v=(2,−5,−2) and w=(a,2,−1) a) Show that u and v are orthogonal. b) Find the value of a for which w is orthogonal to v c) Find proj_v u and proj_w u.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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Suppose u=(1,−2,6)  v=(2,−5,−2) and w=(a,2,−1)

a) Show that u and v are orthogonal.

b) Find the value of a for which w is orthogonal to v

c) Find proj_v u and proj_w u.

d) Find ∥ proj_v u ∥ and ∥ proj_w u ∥.

 both a,b,c,d

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